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#ifndef PCL_REGISTRATION_NDT_OMP_H_
#define PCL_REGISTRATION_NDT_OMP_H_

#include <pcl/registration/registration.h>
#include "voxel_grid_covariance_omp.h"

#include <unsupported/Eigen/NonLinearOptimization>

namespace ndt_omp
{
enum NeighborSearchMethod { KDTREE, DIRECT26, DIRECT7, DIRECT1 };

/** \brief A 3D Normal Distribution Transform registration implementation for point cloud data.
 * \note For more information please see
 * <b>Magnusson, M. (2009). The Three-Dimensional Normal-Distributions Transform —
 * an Efﬁcient Representation for Registration, Surface Analysis, and Loop Detection.
 * PhD thesis, Orebro University. Orebro Studies in Technology 36.</b>,
 * <b>More, J., and Thuente, D. (1994). Line Search Algorithm with Guaranteed Sufficient Decrease
 * In ACM Transactions on Mathematical Software.</b> and
 * Sun, W. and Yuan, Y, (2006) Optimization Theory and Methods: Nonlinear Programming. 89-100
 * \note Math refactored by Todor Stoyanov.
 * \author Brian Okorn (Space and Naval Warfare Systems Center Pacific)
 */
template <typename PointSource, typename PointTarget>
class NormalDistributionsTransform : public pcl::Registration<PointSource, PointTarget>
{
protected:
  typedef typename pcl::Registration<PointSource, PointTarget>::PointCloudSource PointCloudSource;
  typedef typename PointCloudSource::Ptr PointCloudSourcePtr;
  typedef typename PointCloudSource::ConstPtr PointCloudSourceConstPtr;

  typedef typename pcl::Registration<PointSource, PointTarget>::PointCloudTarget PointCloudTarget;
  typedef typename PointCloudTarget::Ptr PointCloudTargetPtr;
  typedef typename PointCloudTarget::ConstPtr PointCloudTargetConstPtr;

  typedef pcl::PointIndices::Ptr PointIndicesPtr;
  typedef pcl::PointIndices::ConstPtr PointIndicesConstPtr;

  /** \brief Typename of searchable voxel grid containing mean and covariance. */
  typedef ndt_omp::VoxelGridCovariance<PointTarget> TargetGrid;
  /** \brief Typename of pointer to searchable voxel grid. */
  typedef TargetGrid * TargetGridPtr;
  /** \brief Typename of const pointer to searchable voxel grid. */
  typedef const TargetGrid * TargetGridConstPtr;
  /** \brief Typename of const pointer to searchable voxel grid leaf. */
  typedef typename TargetGrid::LeafConstPtr TargetGridLeafConstPtr;

public:
  typedef boost::shared_ptr<NormalDistributionsTransform<PointSource, PointTarget> > Ptr;
  typedef boost::shared_ptr<const NormalDistributionsTransform<PointSource, PointTarget> > ConstPtr;

  /** \brief Constructor.
   * Sets \ref outlier_ratio_ to 0.35, \ref step_size_ to 0.05 and \ref resolution_ to 1.0
   */
  NormalDistributionsTransform();

  /** \brief Empty destructor */
  virtual ~NormalDistributionsTransform() {}

  inline void setNumThreads(int n) { num_threads_ = n; }

  inline int getNumThreads() const { return (num_threads_); }

  /** \brief Provide a pointer to the input target (e.g., the point cloud that we want to align the input source to).
   * \param[in] cloud the input point cloud target
   */
  inline void setInputTarget(const PointCloudTargetConstPtr & cloud)
  {
    pcl::Registration<PointSource, PointTarget>::setInputTarget(cloud);
    init();
  }

  /** \brief Set/change the voxel grid resolution.
   * \param[in] resolution side length of voxels
   */
  inline void setResolution(float resolution)
  {
    // Prevents unnessary voxel initiations
    if (resolution_ != resolution) {
      resolution_ = resolution;
      if (input_) init();
    }
  }

  /** \brief Get voxel grid resolution.
   * \return side length of voxels
   */
  inline float getResolution() const { return (resolution_); }

  /** \brief Get the newton line search maximum step length.
   * \return maximum step length
   */
  inline double getStepSize() const { return (step_size_); }

  /** \brief Set/change the newton line search maximum step length.
   * \param[in] step_size maximum step length
   */
  inline void setStepSize(double step_size) { step_size_ = step_size; }

  /** \brief Get the point cloud outlier ratio.
   * \return outlier ratio
   */
  inline double getOulierRatio() const { return (outlier_ratio_); }

  /** \brief Set/change the point cloud outlier ratio.
   * \param[in] outlier_ratio outlier ratio
   */
  inline void setOulierRatio(double outlier_ratio) { outlier_ratio_ = outlier_ratio; }

  inline void setNeighborhoodSearchMethod(NeighborSearchMethod method) { search_method = method; }

  inline NeighborSearchMethod getNeighborhoodSearchMethod() const { return (search_method); }

  /** \brief Get the registration alignment probability.
   * \return transformation probability
   */
  inline double getTransformationProbability() const { return (trans_probability_); }

  /** \brief Get the number of iterations required to calculate alignment.
   * \return final number of iterations
   */
  inline int getFinalNumIteration() const { return (nr_iterations_); }

  /** \brief Return the hessian matrix */
  inline Eigen::Matrix<double, 6, 6> getHessian() const { return hessian_; }

  /** \brief Return the transformation array*/
  inline const std::vector<Eigen::Matrix4f> getFinalTransformationArray() const
  {
    return transformation_array_;
  }

  /** \brief Convert 6 element transformation vector to affine transformation.
   * \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
   * \param[out] trans affine transform corresponding to given transfomation vector
   */
  static void convertTransform(const Eigen::Matrix<double, 6, 1> & x, Eigen::Affine3f & trans)
  {
    trans = Eigen::Translation<float, 3>(float(x(0)), float(x(1)), float(x(2))) *
            Eigen::AngleAxis<float>(float(x(3)), Eigen::Vector3f::UnitX()) *
            Eigen::AngleAxis<float>(float(x(4)), Eigen::Vector3f::UnitY()) *
            Eigen::AngleAxis<float>(float(x(5)), Eigen::Vector3f::UnitZ());
  }

  /** \brief Convert 6 element transformation vector to transformation matrix.
   * \param[in] x transformation vector of the form [x, y, z, roll, pitch, yaw]
   * \param[out] trans 4x4 transformation matrix corresponding to given transfomation vector
   */
  static void convertTransform(const Eigen::Matrix<double, 6, 1> & x, Eigen::Matrix4f & trans)
  {
    Eigen::Affine3f _affine;
    convertTransform(x, _affine);
    trans = _affine.matrix();
  }

  // negative log likelihood function
  // lower is better
  double calculateScore(const PointCloudSource & cloud) const;

protected:
  using pcl::Registration<PointSource, PointTarget>::reg_name_;
  using pcl::Registration<PointSource, PointTarget>::getClassName;
  using pcl::Registration<PointSource, PointTarget>::input_;
  using pcl::Registration<PointSource, PointTarget>::indices_;
  using pcl::Registration<PointSource, PointTarget>::target_;
  using pcl::Registration<PointSource, PointTarget>::nr_iterations_;
  using pcl::Registration<PointSource, PointTarget>::max_iterations_;
  using pcl::Registration<PointSource, PointTarget>::previous_transformation_;
  using pcl::Registration<PointSource, PointTarget>::final_transformation_;
  using pcl::Registration<PointSource, PointTarget>::transformation_;
  using pcl::Registration<PointSource, PointTarget>::transformation_epsilon_;
  using pcl::Registration<PointSource, PointTarget>::converged_;
  using pcl::Registration<PointSource, PointTarget>::corr_dist_threshold_;
  using pcl::Registration<PointSource, PointTarget>::inlier_threshold_;

  using pcl::Registration<PointSource, PointTarget>::update_visualizer_;

  /** \brief Estimate the transformation and returns the transformed source (input) as output.
   * \param[out] output the resultant input transfomed point cloud dataset
   */
  virtual void computeTransformation(PointCloudSource & output)
  {
    computeTransformation(output, Eigen::Matrix4f::Identity());
  }

  /** \brief Estimate the transformation and returns the transformed source (input) as output.
   * \param[out] output the resultant input transfomed point cloud dataset
   * \param[in] guess the initial gross estimation of the transformation
   */
  virtual void computeTransformation(PointCloudSource & output, const Eigen::Matrix4f & guess);

  /** \brief Initiate covariance voxel structure. */
  void inline init()
  {
    target_cells_.setLeafSize(resolution_, resolution_, resolution_);
    target_cells_.setInputCloud(target_);
    // Initiate voxel structure.
    target_cells_.filter(true);
  }

  /** \brief Compute derivatives of probability function w.r.t. the transformation vector.
   * \note Equation 6.10, 6.12 and 6.13 [Magnusson 2009].
   * \param[out] score_gradient the gradient vector of the probability function w.r.t. the transformation vector
   * \param[out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
   * \param[in] trans_cloud transformed point cloud
   * \param[in] p the current transform vector
   * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
   */
  double computeDerivatives(
    Eigen::Matrix<double, 6, 1> & score_gradient, Eigen::Matrix<double, 6, 6> & hessian,
    PointCloudSource & trans_cloud, Eigen::Matrix<double, 6, 1> & p, bool compute_hessian = true);

  /** \brief Compute individual point contirbutions to derivatives of probability function w.r.t. the transformation
   * vector. \note Equation 6.10, 6.12 and 6.13 [Magnusson 2009]. \param[in,out] score_gradient the gradient vector of
   * the probability function w.r.t. the transformation vector \param[in,out] hessian the hessian matrix of the
   * probability function w.r.t. the transformation vector \param[in] x_trans transformed point minus mean of occupied
   * covariance voxel \param[in] c_inv covariance of occupied covariance voxel \param[in] compute_hessian flag to
   * calculate hessian, unnessissary for step calculation.
   */
  double updateDerivatives(
    Eigen::Matrix<double, 6, 1> & score_gradient, Eigen::Matrix<double, 6, 6> & hessian,
    const Eigen::Matrix<float, 4, 6> & point_gradient_,
    const Eigen::Matrix<float, 24, 6> & point_hessian_, const Eigen::Vector3d & x_trans,
    const Eigen::Matrix3d & c_inv, bool compute_hessian = true) const;

  /** \brief Precompute anglular components of derivatives.
   * \note Equation 6.19 and 6.21 [Magnusson 2009].
   * \param[in] p the current transform vector
   * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
   */
  void computeAngleDerivatives(Eigen::Matrix<double, 6, 1> & p, bool compute_hessian = true);

  /** \brief Compute point derivatives.
   * \note Equation 6.18-21 [Magnusson 2009].
   * \param[in] x point from the input cloud
   * \param[in] compute_hessian flag to calculate hessian, unnessissary for step calculation.
   */
  void computePointDerivatives(
    Eigen::Vector3d & x, Eigen::Matrix<double, 3, 6> & point_gradient_,
    Eigen::Matrix<double, 18, 6> & point_hessian_, bool compute_hessian = true) const;

  void computePointDerivatives(
    Eigen::Vector3d & x, Eigen::Matrix<float, 4, 6> & point_gradient_,
    Eigen::Matrix<float, 24, 6> & point_hessian_, bool compute_hessian = true) const;

  /** \brief Compute hessian of probability function w.r.t. the transformation vector.
   * \note Equation 6.13 [Magnusson 2009].
   * \param[out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
   * \param[in] trans_cloud transformed point cloud
   * \param[in] p the current transform vector
   */
  void computeHessian(
    Eigen::Matrix<double, 6, 6> & hessian, PointCloudSource & trans_cloud,
    Eigen::Matrix<double, 6, 1> & p);

  /** \brief Compute individual point contirbutions to hessian of probability function w.r.t. the transformation vector.
   * \note Equation 6.13 [Magnusson 2009].
   * \param[in,out] hessian the hessian matrix of the probability function w.r.t. the transformation vector
   * \param[in] x_trans transformed point minus mean of occupied covariance voxel
   * \param[in] c_inv covariance of occupied covariance voxel
   */
  void updateHessian(
    Eigen::Matrix<double, 6, 6> & hessian, const Eigen::Matrix<double, 3, 6> & point_gradient_,
    const Eigen::Matrix<double, 18, 6> & point_hessian_, const Eigen::Vector3d & x_trans,
    const Eigen::Matrix3d & c_inv) const;

  /** \brief Compute line search step length and update transform and probability derivatives using More-Thuente method.
   * \note Search Algorithm [More, Thuente 1994]
   * \param[in] x initial transformation vector, \f$ x \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ \vec{p} \f$ in
   * Algorithm 2 [Magnusson 2009] \param[in] step_dir descent direction, \f$ p \f$ in Equation 1.3 (Moore, Thuente 1994)
   * and \f$ \delta \vec{p} \f$ normalized in Algorithm 2 [Magnusson 2009] \param[in] step_init initial step length
   * estimate, \f$ \alpha_0 \f$ in Moore-Thuente (1994) and the noramal of \f$ \delta \vec{p} \f$ in Algorithm 2
   * [Magnusson 2009] \param[in] step_max maximum step length, \f$ \alpha_max \f$ in Moore-Thuente (1994) \param[in]
   * step_min minimum step length, \f$ \alpha_min \f$ in Moore-Thuente (1994) \param[out] score final score function
   * value, \f$ f(x + \alpha p) \f$ in Equation 1.3 (Moore, Thuente 1994) and \f$ score \f$ in Algorithm 2 [Magnusson
   * 2009] \param[in,out] score_gradient gradient of score function w.r.t. transformation vector, \f$ f'(x + \alpha p)
   * \f$ in Moore-Thuente (1994) and \f$ \vec{g} \f$ in Algorithm 2 [Magnusson 2009] \param[out] hessian hessian of
   * score function w.r.t. transformation vector, \f$ f''(x + \alpha p) \f$ in Moore-Thuente (1994) and \f$ H \f$ in
   * Algorithm 2 [Magnusson 2009] \param[in,out] trans_cloud transformed point cloud, \f$ X \f$ transformed by \f$
   * T(\vec{p},\vec{x}) \f$ in Algorithm 2 [Magnusson 2009] \return final step length
   */
  double computeStepLengthMT(
    const Eigen::Matrix<double, 6, 1> & x, Eigen::Matrix<double, 6, 1> & step_dir, double step_init,
    double step_max, double step_min, double & score, Eigen::Matrix<double, 6, 1> & score_gradient,
    Eigen::Matrix<double, 6, 6> & hessian, PointCloudSource & trans_cloud);

  /** \brief Update interval of possible step lengths for More-Thuente method, \f$ I \f$ in More-Thuente (1994)
   * \note Updating Algorithm until some value satifies \f$ \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$
   * and Modified Updating Algorithm from then on [More, Thuente 1994].
   * \param[in,out] a_l first endpoint of interval \f$ I \f$, \f$ \alpha_l \f$ in Moore-Thuente (1994)
   * \param[in,out] f_l value at first endpoint, \f$ f_l \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_l) \f$ for Update
   * Algorithm and \f$ \phi(\alpha_l) \f$ for Modified Update Algorithm \param[in,out] g_l derivative at first endpoint,
   * \f$ g_l \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_l) \f$ for Update Algorithm and \f$ \phi'(\alpha_l) \f$ for
   * Modified Update Algorithm \param[in,out] a_u second endpoint of interval \f$ I \f$, \f$ \alpha_u \f$ in
   * Moore-Thuente (1994) \param[in,out] f_u value at second endpoint, \f$ f_u \f$ in Moore-Thuente (1994), \f$
   * \psi(\alpha_u) \f$ for Update Algorithm and \f$ \phi(\alpha_u) \f$ for Modified Update Algorithm \param[in,out] g_u
   * derivative at second endpoint, \f$ g_u \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_u) \f$ for Update Algorithm
   * and \f$ \phi'(\alpha_u) \f$ for Modified Update Algorithm \param[in] a_t trial value, \f$ \alpha_t \f$ in
   * Moore-Thuente (1994) \param[in] f_t value at trial value, \f$ f_t \f$ in Moore-Thuente (1994), \f$ \psi(\alpha_t)
   * \f$ for Update Algorithm and \f$ \phi(\alpha_t) \f$ for Modified Update Algorithm \param[in] g_t derivative at
   * trial value, \f$ g_t \f$ in Moore-Thuente (1994), \f$ \psi'(\alpha_t) \f$ for Update Algorithm and \f$
   * \phi'(\alpha_t) \f$ for Modified Update Algorithm \return if interval converges
   */
  bool updateIntervalMT(
    double & a_l, double & f_l, double & g_l, double & a_u, double & f_u, double & g_u, double a_t,
    double f_t, double g_t);

  /** \brief Select new trial value for More-Thuente method.
   * \note Trial Value Selection [More, Thuente 1994], \f$ \psi(\alpha_k) \f$ is used for \f$ f_k \f$ and \f$ g_k \f$
   * until some value satifies the test \f$ \psi(\alpha_k) \leq 0 \f$ and \f$ \phi'(\alpha_k) \geq 0 \f$
   * then \f$ \phi(\alpha_k) \f$ is used from then on.
   * \note Interpolation Minimizer equations from Optimization Theory and Methods: Nonlinear Programming By Wenyu Sun,
   * Ya-xiang Yuan (89-100). \param[in] a_l first endpoint of interval \f$ I \f$, \f$ \alpha_l \f$ in Moore-Thuente
   * (1994) \param[in] f_l value at first endpoint, \f$ f_l \f$ in Moore-Thuente (1994) \param[in] g_l derivative at
   * first endpoint, \f$ g_l \f$ in Moore-Thuente (1994) \param[in] a_u second endpoint of interval \f$ I \f$, \f$
   * \alpha_u \f$ in Moore-Thuente (1994) \param[in] f_u value at second endpoint, \f$ f_u \f$ in Moore-Thuente (1994)
   * \param[in] g_u derivative at second endpoint, \f$ g_u \f$ in Moore-Thuente (1994)
   * \param[in] a_t previous trial value, \f$ \alpha_t \f$ in Moore-Thuente (1994)
   * \param[in] f_t value at previous trial value, \f$ f_t \f$ in Moore-Thuente (1994)
   * \param[in] g_t derivative at previous trial value, \f$ g_t \f$ in Moore-Thuente (1994)
   * \return new trial value
   */
  double trialValueSelectionMT(
    double a_l, double f_l, double g_l, double a_u, double f_u, double g_u, double a_t, double f_t,
    double g_t);

  /** \brief Auxilary function used to determin endpoints of More-Thuente interval.
   * \note \f$ \psi(\alpha) \f$ in Equation 1.6 (Moore, Thuente 1994)
   * \param[in] a the step length, \f$ \alpha \f$ in More-Thuente (1994)
   * \param[in] f_a function value at step length a, \f$ \phi(\alpha) \f$ in More-Thuente (1994)
   * \param[in] f_0 initial function value, \f$ \phi(0) \f$ in Moore-Thuente (1994)
   * \param[in] g_0 initial function gradiant, \f$ \phi'(0) \f$ in More-Thuente (1994)
   * \param[in] mu the step length, constant \f$ \mu \f$ in Equation 1.1 [More, Thuente 1994]
   * \return sufficent decrease value
   */
  inline double auxilaryFunction_PsiMT(
    double a, double f_a, double f_0, double g_0, double mu = 1.e-4)
  {
    return (f_a - f_0 - mu * g_0 * a);
  }

  /** \brief Auxilary function derivative used to determin endpoints of More-Thuente interval.
   * \note \f$ \psi'(\alpha) \f$, derivative of Equation 1.6 (Moore, Thuente 1994)
   * \param[in] g_a function gradient at step length a, \f$ \phi'(\alpha) \f$ in More-Thuente (1994)
   * \param[in] g_0 initial function gradiant, \f$ \phi'(0) \f$ in More-Thuente (1994)
   * \param[in] mu the step length, constant \f$ \mu \f$ in Equation 1.1 [More, Thuente 1994]
   * \return sufficent decrease derivative
   */
  inline double auxilaryFunction_dPsiMT(double g_a, double g_0, double mu = 1.e-4)
  {
    return (g_a - mu * g_0);
  }

  /** \brief The voxel grid generated from target cloud containing point means and covariances. */
  TargetGrid target_cells_;

  // double fitness_epsilon_;

  /** \brief The side length of voxels. */
  float resolution_;

  /** \brief The maximum step length. */
  double step_size_;

  /** \brief The ratio of outliers of points w.r.t. a normal distribution, Equation 6.7 [Magnusson 2009]. */
  double outlier_ratio_;

  /** \brief The normalization constants used fit the point distribution to a normal distribution, Equation 6.8
   * [Magnusson 2009]. */
  double gauss_d1_, gauss_d2_, gauss_d3_;

  /** \brief The probability score of the transform applied to the input cloud, Equation 6.9 and 6.10 [Magnusson 2009].
   */
  double trans_probability_;

  /** \brief Precomputed Angular Gradient
   *
   * The precomputed angular derivatives for the jacobian of a transformation vector, Equation 6.19 [Magnusson 2009].
   */
  Eigen::Vector3d j_ang_a_, j_ang_b_, j_ang_c_, j_ang_d_, j_ang_e_, j_ang_f_, j_ang_g_, j_ang_h_;

  Eigen::Matrix<float, 8, 4> j_ang;

  /** \brief Precomputed Angular Hessian
   *
   * The precomputed angular derivatives for the hessian of a transformation vector, Equation 6.19 [Magnusson 2009].
   */
  Eigen::Vector3d h_ang_a2_, h_ang_a3_, h_ang_b2_, h_ang_b3_, h_ang_c2_, h_ang_c3_, h_ang_d1_,
    h_ang_d2_, h_ang_d3_, h_ang_e1_, h_ang_e2_, h_ang_e3_, h_ang_f1_, h_ang_f2_, h_ang_f3_;

  Eigen::Matrix<float, 16, 4> h_ang;

  /** \brief The first order derivative of the transformation of a point w.r.t. the transform vector, \f$ J_E \f$ in
   * Equation 6.18 [Magnusson 2009]. */
  //      Eigen::Matrix<double, 3, 6> point_gradient_;

  /** \brief The second order derivative of the transformation of a point w.r.t. the transform vector, \f$ H_E \f$ in
   * Equation 6.20 [Magnusson 2009]. */
  //      Eigen::Matrix<double, 18, 6> point_hessian_;

  int num_threads_;

  Eigen::Matrix<double, 6, 6> hessian_;
  std::vector<Eigen::Matrix4f> transformation_array_;

public:
  NeighborSearchMethod search_method;

  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
};

}  // namespace ndt_omp

#endif  // PCL_REGISTRATION_NDT_H_
